SORU $1.$ In the system shown in the static equilibrium position, a spring with a spring coefficient $k_1$ is attached to point $A,$ and a spring with a spring coefficient $k_2$ is attached to point B$.$ O is the center of the mass of the homogeneous cylinder. The cylinder is rolling without slipping on the ground. An inextensible rope is wrapped around the cylinder of mass $m$ and radius $R.$ A mass of $M$ is attached to the end of the rope. Obtain the equation of motion of the small amplitude vibrations of the system around the static equilibrium position by constructing the equivalent system.